From these illustrations we derive the following RULE. A. Bring the given denominations to the lowest denomination mentioned, for a numerator. Q. How do you obtain the denominator ? A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator. More Exercises for the Slate. 2. What part of 1 £. is 2 s. 6 d. A. = 3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz. ? A. 398 4. What part of 1 vard is 3 qrs. 3 na. ?. A. tá 5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt. ?** A. 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. 1 gill? A. gota 7. What part of 15 pipes is 25 galls. ? A. g. 8. What part of 2 miles is 7 fur. 11 in. 2 b. c. ? A. 78332 9. What part of 1 month is 19 days ? A. 38. 10. What part of 1 month is 25 days, 13 hours ? A. 918 11. What part of 1 month is 22 days, 15 h. 1 min.?" 9 XLIX. TO REDUCE A FRACTION TO WHOLE Num BERS OF LESS DENOMINATIONS, OR, TO FIND THE VALUE OF A FRACTION. 1. How much is of a shilling? How much It of a lb.' of a lb.? Hoe of a lb. ? it of a lb.? 14 of a Ib.; end of 1 qr. of a cwt. ? ? g? 18? 37? 1 an hour! ? *? Operation by Slate illustrated. 1 What is the value of of a pound ? OPERATION. Q. How do you proNumer. 5 ceed in this example? and why? 20 s. A. Aš 1 £. = 205, Denom. 6)100(16 s. of one pound is iše same as of 20 s., 711], to get of 20, we in iltiply the numerator 5 and 20 together, mak ing 100; which, divid 16 s. 8 d. Ans. 4 ed by the denominator 12 6, gives 16 s. and of another shilling re48 (8 d. maining. This = 48 of 12 d.; then, of 12 d.=8 d. RULE. A. By as many of the next denomination as make one of that; that is, pounds by what makes a pound, ounces by what makes an ounce, as in Reduction of whole numbers. Q. What do you divide the product by ? More Exercises for the Slate. 4. What is the value of any of a pound Troy? A. 10 oz. $ pwts. 167. 5. What is the value of 243 of a hogshead ? A. 49 gallony 12922 qts. 6. What is the value of 371 of a pound avoirdupois? A. 1 lb 1437 i oz. 7. What is the value of 30 of a hogshead? A. 50 gallons. 8. What is the value of 13 of a day? A. 16 hours, 36 min 56 sec. IL, TO REDUCE FRACTIONS OF A HIGHER DENOMINA TION INTO A LOWER. We have seen (1T XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce so £. to the fraction of a penny. 1 In this example, we multi OPERATION. ply the 1, in ato, as in Re Numer. 1 duction of whole numbers 20 s. viz., pounds by what makes a pound, shillings by what 20 makes a shilling, &c. But 12 d. this operation may be express ed differently, thus ; 450 X New numer. 240 20 x 12= 48= d.; or, by dividing the denominators, Then, 240 thus; 20020=24:12= =fd. Ans. Denom. 4801 . 1 d., Ans., as before, in its est terms. RULE. A. Multiply the fraction, as in Reduction ut whole numbers. More Exercises for the Slate. 2. Reduce zło of a pound to the fraction of a shilling. A. The 3. Reduce 1920 of a pound to the fraction of a farthing. A. 4. Reduce Tots of a hogshead to the fraction of a gallon. A. To gas 5. Reduce TýT of a bushel to the fraction of a quart. 4. Iff gt 6. Reduce 1117 of a day to the fraction of a minute. A. 1941 m. 7. Reduce Tomg of a cwt. to the fraction of a pound. A. & I 8. Reduce bio of a hhd. to the fraction of a pint. A. pt. 9. Reduce T&o of a pound to the fraction of a shilling. DIKON ILI. TO REDUCE FRACTIONS OF A LOT TION INTO A EJCEER We have seen, that, to & Tide a fract. II. *? En multiply the denominator, or CITde e EZ This rule is the re rerse of the as, TL, 2RC PETE duction, I IXIL, TI, PB 17 ty : diride br in Peduction of the num I bers. The same result in de dotzin New denom. 480 ed if performed thus: Then, tšo, Ans. Í *x 12 x2= 5 £., Års. Hence the following RULE. More Exercises for the Slate. 2. Reduce 1 of a shilling to the fraction of a pound. 4. zo £. 3. Reduce 1 of a farthing to the fraction of a pound. A. 1920 £. 4. Reduce It of a gallon to the fraction of a hogshead. A. Tobg hhd. 5. Reduce 144 of a quart to the fraction of a bushel. A. bu. 6. Reduce 1411 of a minute to the fraction of a day. A. TALT: 9. Reduce ☆ of a pound to the fraction of a hundred weight. A. Toor 8. Reduce of a pint to the fraction of a hogshead. A. 2520 =oto. 9. Reduce of a shilling to the fraction of a pound. A. O DECIMAL FRACTIONS. 9 LII. Q. When such fractions as these occur, viz. So, ifra 73 , how is a unit supposed to be divided ? A. Into 10 equal parts, called tenths; and each tenth into 10 other equal parts, called hundredths, and each hundredth into 10 more equal parts, called thousandths, &c. Q. How is it customary to write such expressions ? A. By taking away the denominator, and placing a comma before the numerator. Let me see you write down, in this manner, or, too, ooo Q. What name do you give to fractions written in this manner ? A. From the Latin word decem, signifying ten; because they increase and decrease in a tenfold proportion, like whole numbers. Q. What are all other fractions called ? Q. In whole numbers, we are accustomed to call the right-hand figure, units, from which we begin to reckon no cumerate; hence it was found convenient to make the swille piace a starting point in decimals, and to do this, we make use of a comma; what, then, is the use of this comma ? A. It merely shows where the units' place is. A. Because it separates the decimals from the whole numbers. Q. What is the first figure at the right of the separatrix called ? |